Most spectrometers use diffraction gratings to spread out the light so that it can be analyzed into its constituent wavelengths. This light is then focused onto a detector comprised of a linear array of individual detector pixels. The light that strikes a particular pixel is determined by the angle by which the light departs the diffraction grating. This angle is related to the light's wavelength by the well-known diffraction grating equation d*sin θm=m*λ, where d is the grating spacing, θm is the diffraction angle, m is an integer, and A is the wavelength. With d being a fixed property of the diffraction grating, it can be seen that a given angle (and thus a given pixel) corresponds to multiple wavelengths, each paired with a different integer values m.
Conventional diffraction gratings are designed so that most of the light striking the grating and proceeding to the detector winds up in the “first-order beam”, which corresponds to m=1. In the ideal case of no light in the higher order beams (m>1) the light arriving at the detector from the diffraction grating has a unique correspondence between the wavelength λ and the angle θ (and thus the detector pixels). However, some amount of light forms a second-order beam so that the light striking a particular pixel can be a combination of light from the first- and second-order beams. For example, the pixel that receives λ=760 nm first-order (m=1) light might also receive λ=380 nm second-order (m=2) light. Light of different wavelengths is indistinguishable to the detector pixels, so the resultant intensity of light detected by the pixel (and thus reported to the user by the spectrometer) is an unknown mixture of the two wavelengths. Because the purpose of any optical spectrometer is to measure the intensity of light as a function of wavelength, this mixing of light of different wavelengths is a source of error.
Additionally, spectrometers are operated over all or most of the wavelength range of 380-1050 nm, which is the overlap of the effective wavelength range of silicon-based array detectors (200-1050 nm) and tungsten-halogen light sources (380-2000 nm). Embodiments described herein correct errors due to the presence of second-order light using a method of correcting for second-order diffraction effects in spectrometers by processing the spectrometer output that contains the second-order diffraction response, i.e., without having to remove the second-order diffraction with costly optical filters.
To avoid the problem of second-order diffraction, some spectrometers simply measure over less than a factor of two in wavelength range (e.g., 400-800 nm) and restrict shorter wavelengths from entering the spectrometer (or at least reaching the detector). Since many spectrometer uses require a greater wavelength range than allowed by this method, most miniature spectrometers block second-order light from reaching the detector array by aligning a linearly-graded optical high-pass filter in front of the array. The high-pass cutoff of the filter must be graded along the direction of the detector array because different pixels detect different wavelengths and thus require different second-order light to be either passed or filtered out.
Linearly-graded high-pass filters work well to remove second-order light in practice and are manufactured into tens of thousands of spectrometers a year. However, the linear grading makes the filters expensive to produce (approximately $100 each) and they require careful alignment to the detector during the spectrometer's manufacture. Alternatively, US US2013/0258333 to Chalmers et. al, describes a method for inserting small filters over the sensor element to deduce the effects of second order diffraction. However, what is needed is a low-cost effective solution not requiring physical modification of the spectrometer.